A consistent estimator for confounding strength
Regression on observational data can fail to capture a causal relationship in the presence of unobserved confounding. Confounding strength measures this mismatch, but estimating it requires itself additional assumptions. A common assumption is the independence of causal mechanisms, which relies on concentration phenomena in high dimensions. While high dimensions enable the estimation of confounding strength, they also necessitate adapted estimators. In this paper, we derive the asymptotic behavior of the confounding strength estimator by Janzing and Schölkopf (2018) and show that it is generally not consistent. We then use tools from random matrix theory to derive an adapted, consistent estimator.
Authors
- Debarghya Ghoshdastidar (ORCID: https://orcid.org/0000-0003-0202-7007)
- Leena Chennuru Vankadara (ORCID: https://orcid.org/0000-0002-3810-840X)
- Luca Rendsburg (ORCID: https://orcid.org/0000-0001-6561-831X)
- Ulrike von Luxburg
Institutions
- Technical University of Munich (DE)
- University of Tübingen (DE)
Publication Details
- Journal
- Mathematical Statistics and Learning
- Published
- 2024-10-13
- DOI
- https://doi.org/10.4171/msl/47
- Primary Topic
- Health Systems, Economic Evaluations, Quality of Life
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- International Max Planck Research School for Environmental, Cellular and Molecular Microbiology
- Deutsche Forschungsgemeinschaft
- Bundesministerium für Bildung und Forschung
- International Max Planck Research School for Advanced Methods in Process and Systems Engineering